Answer All the Questions

Econ 301 Midterm II

Fall 2011

Hakan Berument

Answer all the questions

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Question 1: Use the Eviews file sleep75. Consider the following model

Sleep = β0 + β1 totwrk + β2 educ + β3 age + β4 age2+ β5 male + u

Sleep is total minutes per week spend sleeping at night; totwrk is total weekly minutes spent working, educ and age are measured in years, male is a variable takes the value of 1 if agent is male, 0 otherwise.

Dependent Variable: SLEEP
Method: Least Squares
Date: 12/20/11 Time: 19:09
Sample: 1 706
Included observations: 706
Variable / Coefficient / Std. Error / t-Statistic / Prob.
C / 3840.832 / 235.1087 / 16.33641 / 0.0000
TOTWRK / -0.163423 / 0.018132 / -9.012918 / 0.0000
EDUC / -11.71332 / 5.866886 / -1.996514 / 0.0463
AGE / -8.696676 / 11.20746 / -0.775972 / 0.4380
AGE2 / 0.128435 / 0.133895 / 0.959222 / 0.3378
MALE / 87.75243 / 34.32616 / 2.556430 / 0.0108
R-squared / 0.122753 / Mean dependent var / 3266.356
Adjusted R-squared / 0.116487 / S.D. dependent var / 444.4134
S.E. of regression / 417.7282 / Akaike info criterion / 14.91600
Sum squared resid / 1.22E+08 / Schwarz criterion / 14.95475
Log likelihood / -5259.348 / Hannan-Quinn criter. / 14.93097
F-statistic / 19.59011 / Durbin-Watson stat / 1.938465
Prob(F-statistic) / 0.000000

1. What is R2, how can you interpret this.?

12.2753 % of variation in sleep is explained by the RHS variables totwrk educ age age2 male.

1. What is the interpretation of the estimated coefficient for β2?

As education increases by 1 unit you expect to see an decreases in sleep by 11.71332 once everything else given (Ceteris paribus)

For the following part report the test statistics and write if you can you reject the null at 5% level?

1. Test if gender makes a difference for sleeping?

Ho: β5 = 3 Ha: not Ho

(87.75243 – 5 ) / 34.32616 = 2.410769 İt is above the critical value of 1.96 thus we reject the null

Alternatively

Restricted model is

Dependent Variable: SLEEP-5*MALE
Method: Least Squares
Date: 12/20/11 Time: 19:22
Sample: 1 706
Included observations: 706
Variable / Coefficient / Std. Error / t-Statistic / Prob.
C / 3840.509 / 235.9142 / 16.27926 / 0.0000
TOTWRK / -0.147000 / 0.016861 / -8.718209 / 0.0000
EDUC / -11.12732 / 5.881932 / -1.891779 / 0.0589
AGE / -8.671083 / 11.24585 / -0.771047 / 0.4409
AGE2 / 0.130796 / 0.134351 / 0.973545 / 0.3306
R-squared / 0.115851 / Mean dependent var / 3263.523
Adjusted R-squared / 0.110806 / S.D. dependent var / 444.5094
S.E. of regression / 419.1594 / Akaike info criterion / 14.92144
Sum squared resid / 1.23E+08 / Schwarz criterion / 14.95373
Log likelihood / -5262.267 / Hannan-Quinn criter. / 14.93391
F-statistic / 22.96320 / Durbin-Watson stat / 1.938696
Prob(F-statistic) / 0.000000
SSR / n / k
Unrestriceted / 1.22E+08 / 706 / 6
Restricted / 1.23E+08 / 706 / 5 / F / 1000000 / = / 5.737705
174285.7

5,73 > 3.84 (F1,700) thus we reject the null

1. Test if age makes a difference for sleeping?

Ho: β3 = β4 = 0 Ha: not Ho

The restricted model is

Dependent Variable: SLEEP
Method: Least Squares
Date: 12/20/11 Time: 19:27
Sample: 1 706
Included observations: 706
Variable / Coefficient / Std. Error / t-Statistic / Prob.
C / 3747.517 / 81.00609 / 46.26217 / 0.0000
TOTWRK / -0.167339 / 0.017937 / -9.329260 / 0.0000
EDUC / -13.88479 / 5.657573 / -2.454196 / 0.0144
MALE / 90.96919 / 34.27441 / 2.654143 / 0.0081
R-squared / 0.119277 / Mean dependent var / 3266.356
Adjusted R-squared / 0.115514 / S.D. dependent var / 444.4134
S.E. of regression / 417.9581 / Akaike info criterion / 14.91429
Sum squared resid / 1.23E+08 / Schwarz criterion / 14.94012
Log likelihood / -5260.744 / Hannan-Quinn criter. / 14.92427
F-statistic / 31.69094 / Durbin-Watson stat / 1.948190
Prob(F-statistic) / 0.000000
SSR / n / k
Unrestriceted / 1.22E+08 / 706 / 6
Restricted / 1.23E+08 / 706 / 4 / F / 500000 / = / 2.868852
174285.7

2.87 < 3.00 (F2,700) So we cannot reject the null.

1. Test if this equation is statistically significant

Ho: β1 = β2 = β3 = β4 = β5 = 0 Ha: not Ho

Restricted model is

Dependent Variable: SLEEP
Method: Least Squares
Date: 12/20/11 Time: 19:30
Sample: 1 706
Included observations: 706
Variable / Coefficient / Std. Error / t-Statistic / Prob.
C / 3266.356 / 16.72572 / 195.2894 / 0.0000
R-squared / 0.000000 / Mean dependent var / 3266.356
Adjusted R-squared / 0.000000 / S.D. dependent var / 444.4134
S.E. of regression / 444.4134 / Akaike info criterion / 15.03280
Sum squared resid / 1.39E+08 / Schwarz criterion / 15.03926
Log likelihood / -5305.580 / Hannan-Quinn criter. / 15.03530
Durbin-Watson stat / 1.918480
SSR / n / k
Unrestriceted / 1.22E+08 / 706 / 6
Restricted / 1.39E+08 / 706 / 1 / F / 3400000 / = / 19.5082
174285.7

19,51 > 2.21 (F5,700) so we reject the null.

1. Test if this equation is statistically significant

Ho: β1 = β2 = β3 = β4 = β5 and Ha: not Ho

Restricted model is

Dependent Variable: SLEEP
Method: Least Squares
Date: 12/21/11 Time: 16:35
Sample: 1 706
Included observations: 706
Variable / Coefficient / Std. Error / t-Statistic / Prob.
C / 3474.663 / 51.07326 / 68.03291 / 0.0000
TOTWRK+EDUC+AGE+AGE2+MALE / -0.054671 / 0.012684 / -4.310340 / 0.0000
R-squared / 0.025712 / Mean dependent var / 3266.356
Adjusted R-squared / 0.024328 / S.D. dependent var / 444.4134
S.E. of regression / 438.9743 / Akaike info criterion / 15.00959
Sum squared resid / 1.36E+08 / Schwarz criterion / 15.02250
Log likelihood / -5296.384 / Hannan-Quinn criter. / 15.01458
F-statistic / 18.57903 / Durbin-Watson stat / 1.954978
Prob(F-statistic) / 0.000019
SSR / n / k
Unrestriceted / 1.22E+08 / 706 / 6
Restricted / 1.36E+08 / 706 / 2 / F / 3500000 / = / 20.08197
174285.7

F statistics 20.08 is greater than 2.37 (F4,700) so we reject the null.

1. Test

Ho: 2 β2 = β3 = 4β4 and Ha: not Ho

The restricted model is

Dependent Variable: SLEEP
Method: Least Squares
Date: 12/21/11 Time: 16:42
Sample: 1 706
Included observations: 706
Variable / Coefficient / Std. Error / t-Statistic / Prob.
C / 3512.227 / 48.91377 / 71.80445 / 0.0000
TOTWRK / -0.165164 / 0.018018 / -9.166810 / 0.0000
2*EDUC+AGE+4*AGE2 / 0.008576 / 0.004152 / 2.065494 / 0.0392
MALE / 84.91865 / 34.35833 / 2.471559 / 0.0137
R-squared / 0.117087 / Mean dependent var / 3266.356
Adjusted R-squared / 0.113314 / S.D. dependent var / 444.4134
S.E. of regression / 418.4776 / Akaike info criterion / 14.91677
Sum squared resid / 1.23E+08 / Schwarz criterion / 14.94261
Log likelihood / -5261.621 / Hannan-Quinn criter. / 14.92676
F-statistic / 31.03168 / Durbin-Watson stat / 1.940429
Prob(F-statistic) / 0.000000
SSR / n / k
Unrestriceted / 1.22E+08 / 706 / 6
Restricted / 1.23E+08 / 706 / 4 / F / 500000 / = / 2.868852
174285.7

2.68 < 3 (F2,700) so we cannot reject the null.

1. Test

Ho: β2 = 2β3 and β4= 0.5 and Ha: not Ho

The restricted model is

Dependent Variable: SLEEP-0.5*AGE2
Method: Least Squares
Date: 12/21/11 Time: 16:45
Sample: 1 706
Included observations: 706
Variable / Coefficient / Std. Error / t-Statistic / Prob.
C / 4531.438 / 76.93770 / 58.89749 / 0.0000
TOTWRK / -0.156287 / 0.018061 / -8.653295 / 0.0000
EDUC+2*AGE / -19.92155 / 0.717566 / -27.76268 / 0.0000
MALE / 88.74649 / 34.49369 / 2.572832 / 0.0103
R-squared / 0.539004 / Mean dependent var / 2448.783
Adjusted R-squared / 0.537034 / S.D. dependent var / 617.3091
S.E. of regression / 420.0271 / Akaike info criterion / 14.92417
Sum squared resid / 1.24E+08 / Schwarz criterion / 14.95000
Log likelihood / -5264.230 / Hannan-Quinn criter. / 14.93415
F-statistic / 273.5965 / Durbin-Watson stat / 1.927987
Prob(F-statistic) / 0.000000
SSR / n / k
Unrestriceted / 1.22E+08 / 706 / 6
Restricted / 1.24E+08 / 706 / 4 / F / 1000000 / = / 5.737705
174285.7

5,73 3 (F2,700) so we reject the null.

1. Test

Ho: β2 - 2β3 = 4 and β4= 0.5 and Ha: not Ho

The unrestricted model is

Dependent Variable: SLEEP
Method: Least Squares
Date: 12/21/11 Time: 16:48
Sample: 1 706
Included observations: 706
SLEEP= C(11) +C(1) * TOTWRK +C(2)* EDUC +C(3)* AGE +C(4)* AGE2+
C(5)* MALE
Coefficient / Std. Error / t-Statistic / Prob.
C(11) / 3840.832 / 235.1087 / 16.33641 / 0.0000
C(1) / -0.163423 / 0.018132 / -9.012918 / 0.0000
C(2) / -11.71332 / 5.866886 / -1.996514 / 0.0463
C(3) / -8.696676 / 11.20746 / -0.775972 / 0.4380
C(4) / 0.128435 / 0.133895 / 0.959222 / 0.3378
C(5) / 87.75243 / 34.32616 / 2.556430 / 0.0108
R-squared / 0.122753 / Mean dependent var / 3266.356
Adjusted R-squared / 0.116487 / S.D. dependent var / 444.4134
S.E. of regression / 417.7282 / Akaike info criterion / 14.91600
Sum squared resid / 1.22E+08 / Schwarz criterion / 14.95475
Log likelihood / -5259.348 / Hannan-Quinn criter. / 14.93097
F-statistic / 19.59011 / Durbin-Watson stat / 1.938465
Prob(F-statistic) / 0.000000

The restricted model is

Dependent Variable: SLEEP
Method: Least Squares
Date: 12/21/11 Time: 16:50
Sample: 1 706
Included observations: 706
SLEEP= C(11) +C(1) * TOTWRK +(4+2*C(3))* EDUC +C(3)* AGE +0.5*
AGE2+ C(5)* MALE
Coefficient / Std. Error / t-Statistic / Prob.
C(11) / 4978.305 / 107.7539 / 46.20072 / 0.0000
C(1) / -0.149795 / 0.019488 / -7.686465 / 0.0000
C(3) / -35.94654 / 1.525310 / -23.56671 / 0.0000
C(5) / 90.86478 / 37.25946 / 2.438704 / 0.0150
R-squared / -0.036697 / Mean dependent var / 3266.356
Adjusted R-squared / -0.041127 / S.D. dependent var / 444.4134
S.E. of regression / 453.4601 / Akaike info criterion / 15.07734
Sum squared resid / 1.44E+08 / Schwarz criterion / 15.10317
Log likelihood / -5318.301 / Hannan-Quinn criter. / 15.08732
Durbin-Watson stat / 1.931708
SSR / n / k
Unrestriceted / 1.22E+08 / 706 / 6
Restricted / 1.44E+08 / 706 / 4 / F / 11000000 / = / 63.11475
174285.7

63.11 > 3 (F2,700) so we reject the null.

1. Test

Ho: β0+ β5 = 90, β1 = 0.10 and 10 β3= β5and Ha: not Ho

The restricted model is

Dependent Variable: SLEEP
Method: Least Squares
Date: 12/21/11 Time: 16:53
Sample: 1 706
Included observations: 706
SLEEP= 90-10*C(3) +0.1 * TOTWRK +C(2)* EDUC +C(3)* AGE +C(4)*
AGE2+ 10*C(3)* MALE
Coefficient / Std. Error / t-Statistic / Prob.
C(3) / 31.00294 / 4.584331 / 6.762806 / 0.0000
C(2) / 148.3401 / 5.540200 / 26.77521 / 0.0000
C(4) / -0.051516 / 0.066526 / -0.774367 / 0.4390
R-squared / -1.503776 / Mean dependent var / 3266.356
Adjusted R-squared / -1.510899 / S.D. dependent var / 444.4134
S.E. of regression / 704.2094 / Akaike info criterion / 15.95627
Sum squared resid / 3.49E+08 / Schwarz criterion / 15.97564
Log likelihood / -5629.563 / Hannan-Quinn criter. / 15.96376
Durbin-Watson stat / 1.726628
SSR / n / k
Unrestriceted / 1.22E+08 / 706 / 6
Restricted / 3.49E+08 / 706 / 3 / F / 75666667 / = / 434.153
174285.7

434.15 > 2.06 (F3,700) so we reject the null.

1

Econ 301 Midterm II

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